There is a dearth of evidence synthesis on the prevalence of anxiety among university students even though the risk of psychological disorders among this population is quite high. We conducted a quantitative systematic review to estimate the global prevalence of anxiety among university students during the COVID-19 pandemic. A systematic search for cross-sectional studies on PubMed, Scopus, and PsycINFO, using PRISMA guidelines, was conducted from September 2020 to February 2021. A total of 36 studies were included, using a random-effects model to calculate the pooled proportion of anxiety. A meta-analysis of the prevalence estimate of anxiety yielded a summary prevalence of 41% (95% CI = 0.34–0.49), with statistically significant evidence of between-study heterogeneity (Q = 80801.97, I² = 100%, p ≤ 0.0001). A subgroup analysis reported anxiety prevalence in Asia as 33% (95% CI:0.25–0.43), the prevalence of anxiety in Europe as 51% (95% CI: 0.44–0.59), and the highest prevalence of anxiety in the USA as 56% (95% CI: 0.44–0.67). A subgroup gender-based analysis reported the prevalence of anxiety in females as 43% (95% CI:0.29–0.58) compared to males with an anxiety prevalence of 39% (95% CI:0.29–0.50). University students seem to have a high prevalence of anxiety, indicating an increased mental health burden during this pandemic.